In my experience using ArcGIS with PostgreSQL, the support has gotten better and considerably more stable over the years. While I haven’t tested every permutation of ArcGIS, PostgreSQL and PostGIS, you should be safe to use the various components together, as long as you are close to the “official” version. Of course, stick to what is recommended if you are using PostgreSQL in production, especially if you may need support from ESRI.

Naturally, if you are not tied to the ESRI stack, you are more free to choose the PostgreSQL version you would like to use. While I’ve not yet upgraded to PostgreSQL 9.6, I am looking to do so by the end of the calendar year.